Superrotation of upper atmosphere by global deposition of meteoroids

A new theory of the superrotation of upper atmosphere is worked out on the basis of global deposition of meteoroids assuming that a certain constant influx of meteoroids is continually falling upon the Earth's atmosphere. On the average the meteoroids are shown to carry a greater amount of orbital angular momentum than that corresponding to the Earth's orbit about the Sun. It is argued that the excess of orbital angular momentum appears as extra spin angular momentum in the atmospheric layer in which the meteoroids are arrested and this is used to calculate the velocity difference which can be maintained across a certain layer of the atmosphere. It is found that a global deposition of 34 tons/day of meteoric material is required to account for the observed superrotation which agrees with the recent estimates on meteoric mass influx on the Earth.     

Superrotation of the thermosphere by global deposition of meteoroids?

Mitra has suggested that the Superrotation of the upper atmosphere is caused by a deposition of meteoroids. The meteoroids are assumed to impart to the atmosphere the excess of their orbital angular momentum per unit mass over the Earth's angular momentum per unit mass. The process is to take place in the height region above 150 km. Only above this height is a Superrotation of the atmosphere observed. In this report the forces that tend to make the atmosphere corotate with the Earth are analysed. It is shown that the most important of these forces is ion drag, and not viscous drag as postulated by Mitra. As the net angular spin momentum imparted by the meteoroids seems to be less than Mitra's estimate and its main part is applied to the atmosphere at altitudes much lower than 150 km, the hypothesis that meteoroids provide a significant contribution to the Superrotation is rejected.     

Momentum of meteoroids and its effect on the Earth's atmosphere

Recent studies have attributed certain properties of the Earth's atmosphere to excess orbita angular momentum of impinging meteoroids. A realistic analysis of meteor observations does not support the existence of this excess.     

Comment on “superrotation of upper atmosphere by global deposition of meteoroids”: Planet. space sci.22, 559 (1974)

The meteoric influx explanation of superrotation (Mitra, 1974) is re-examined. It is shown that the excess orbital angular momentum of the meteoroids is transferred to the region below about 110 km, and thus can probably not account for the superrotation of the 150–400 km atmospheric layer.     

On the maintenance of thermal wind balance and equatorial superrotation in Titan's stratosphere

Titan's atmospheric winds, like those on Venus, exhibit superrotation at high altitudes. Titan general circulation models have yielded conflicting results on whether prograde winds in excess of 100 m s⁻¹ at the 1 mbar level are possible based on known physical processes that drive wind systems. A comprehensive two-dimensional (2D) model for Titan's stratosphere was constructed to systematically explore the physical mechanisms that produce and maintain stratospheric wind systems. To ensure conservation of angular momentum in the limit of no net exchange of atmospheric angular momentum with the solid satellite and no external sources and sinks, the zonal momentum equation was solved in flux form for total angular momentum. The relationships among thermal wind balance, meridional circulation, and zonal wind were examined with numerical experiments over a range of values for fundamental input parameters, including planetary rotation rate, radius, internal friction due to wave stresses, and net radiative drive. The magnitude of mid-latitude jets is most sensitive to a single parameter, the planetary rotation rate and results from the conversion of planetary angular momentum to relative angular momentum by the meridional circulation, whereas the strength of meridional circulation is mainly determined by the magnitude of the radiative drive. For Titan's slowly rotating atmosphere, the meridional temperature gradient is vanishingly small, even when the radiative drive is enhanced beyond reasonable magnitudes, and can be inferred from zonal winds in gradient/thermal wind balance. In our 2D model large equatorial superrotation in Titan's stratosphere can be only produced through internal drag forcing by eddy momentum fluxes, which redistribute angular momentum within the atmosphere, while still conserving the total angular momentum of the atmosphere with time. We cannot identify any waves, such as gravitational or thermal tides, that are sufficiently capable of generating the required eddy forcing of >50 m s⁻¹ Titan-day⁻¹ to maintain peak prograde winds in excess of 100 m s⁻¹ at the 1 mbar level.     

Co-accretion of the Earth-Moon system after the giant impact: reduction of the total angular momentum by lunar impact ejecta

Though the Moon is considered to have been formed by the so-called giant impact, the mass of the Earth immediately after the impact is still controversial. If the Moon was formed during the Earth's accretion, a subsequent accretion of residual heliocentric planetesimals onto the protoearth and the protomoon must have occurred. In this co-accretion stage, a significant amount of lunar-impact-ejecta would be ejected to circumterrestrial orbits, since the mean impact velocity of the planetesimals with the protomoon is much larger than the escape velocity of the protomoon. Orbital calculations of test particles ejected from the protomoon, whose semimajor axis is smaller than that of the present Moon, reveal that most of the particles escaping from the protomoon also escape from the Hill sphere of the protoearth and reduce the planetocentric angular momentum of the primordial Earth-Moon system. Using the results of the ejecta simulations, we investigate the evolution of the mass ratio and the total angular momentum (Earth's spin angular momentum + Moon's orbital angular momentum) of the Earth-Moon system during the co-accretion. We find that the mass of the protomoon is almost constant or rather decreases and the total angular momentum decreases significantly, if the random velocity of planetesimals is as large as the escape velocity of the protoearth. On the other hand, if the random velocity is the half of the escape velocity of the protoearth, the mass ratio is kept to be almost as large as the present value and the decrease of the total angular momentum is not so significant. Comparing with the results of giant impact simulations, we find that the mass of the protoearth immediately after the Moon-forming impact was 0.7-0.8 times the present value if the impactor-to-target mass ratio was 3:7, whereas the giant impact occurred almost in the end of the Earth's accretion if the impactor-to-target mass ratio was 1:9.     

The Dynamics of Meteoroid streams

Meteors are streaks of light seen in the upper atmosphere when particles from the inter-planetary dust complex collide with the Earth. Meteor showers originate from the impact of a coherent stream of such dust particles, generally assumed to have been recently ejected from a parent comet. The parent comets of these dust particles, or meteoroids, fortunately, for us tend not to collide with the Earth. Hence there has been orbital changes from one to the other so as to cause a relative movement of the nodes of the meteor orbits and that of the comet, implying changes in the energy and/or angular momentum. In this review, we will discuss these changes and their causes and through this place limits on the ejection process. Other forces also come into play in the longer term, for example perturbations from the planets, and the effects of radiation pressure and Poynting–Robertson drag. The effect of these will also be discussed with a view to understanding both the observed evolution in some meteor streams. Finally we will consider the final fate of meteor streams as contributors to the interplanetary dust complex.     

Venus' superrotation,mixing length theory and eddy diffusion: A parametric study

The Hadley mechanism is adopted to describe the axisymmetric four day superrotation in the Venus atmosphere, with solar driven meridional winds redistributing energy and momentum, and eddy diffusion describing the actions of three dimensional transient eddies. We address the question how the eddy diffusion coefficients are related to the properties of the circulation. For the atmosphere of a slowly rotating planet such as Venus, we show that a form of the non-linear closure is suggested by the mixing length hypothesis, which constrains the magnitude of the eddy diffusion coefficients. Combining this constraint with the concept of the Rossby radius of deformation yields zonal velocities on the order of 100 m sec^–1. A steady state, non-linear, one-layer spectral model is used for a parametric study to find a relationship between heat source, meridional circulation and eddy diffusion coefficients, which yields the large zonal velocities observed. This analysis leads to the following conclusions: (1) Proportional changes in the heat source and eddy diffusion coefficients do not significantly change the zonal velocities. (2) The meridional velocity is virtually constant for large eddy diffusion coefficients. (3) Below a threshold in the diffusion rate, the meridional velocity decreases, commensurate with the mixing length hypothesis. Eddy heat conduction becomes important and shares with the Hadley cell advection in balancing the solar heating. The zonal velocities then reach large values near 100 m sec^–1. (4) For large eddy diffusion and small heating rates, the zonal velocities decrease with decreasing planetary rotation rates. However, under condition (3), the zonal velocities are independent of the planetary rotation rate. Ramifications are discussed for related parameterizations in GCMs, emphasizing that eddy diffusion coefficients are governed by solar forcing and cannot be chosen independently.     

The 'silent world' of Comet 15P/Finlay

Comet 15P/Finlay is unusual in that, contrary to ab initio expectations, it demonstrates no apparent linkage to any known meteor shower. Using data contained within the Electronic Atlas of Dynamical Evolutions of Short-Period Comets, we evaluate theoretical shower radiants for Comet 15P/Finlay, but find no evidence to link it to any meteoric anomalies in recorded antiquity. This result, however, must be tempered by the fact that any Comet 15P/Finlay-derived meteoroids will have a low, 16 km s⁻¹, encounter velocity with Earth's atmosphere. Typically, therefore, one would expect mostly faint meteors to be produced during an encounter with a Comet 15P/Finlay-derived meteoroid stream. We have conducted a D -criterion survey of meteoroid orbits derived from three southern hemisphere meteor radar surveys conducted during the 1960s, and again we find no evidence for any Comet 15P/Finlay-related activity. Numerical calculations following the orbital evolution of hypothetical meteoroids ejected from the comet, at each perihelion epoch since 1886, indicate that Jovian perturbations effectively 'drive' the meteoroids to orbits with nodal points beyond the Earth's orbit. The numerical calculations indicate that, even if Comet 15P/Finlay had been a copious emitter of meteoroids during the past 100 years, virtually none of them would have evolved into orbits capable of being sampled by the Earth. There are good observational data, however, to suggest that Comet 15P/Finlay is becoming a transitional comet–asteroid object, and that it has probably not been an efficient producer of meteoroids during the past several hundreds of years.     

The role of tidal interactions in star formation

Nearly all of the initial angular momentum of the matter that goes into each forming star must somehow be removed or redistributed during the formation process. The possible transport mechanisms and the possible fates of the excess angular momentum are discussed, and it is argued that transport processes in discs are probably not sufficient by themselves to solve the angular momentum problem, while tidal interactions with other stars in forming binary or multiple systems are likely to be of very general importance in redistributing angular momentum during the star formation process. Most, if not all, stars probably form in binary or multiple systems, and tidal torques in these systems can transfer much of the angular momentum from the gas around each forming star to the orbital motions of the companion stars. Tidally generated waves in circumstellar discs may contribute to the overall redistribution of angular momentum. Stars may gain much of their mass by tidally triggered bursts of rapid accretion, and these bursts could account for some of the most energetic phenomena of the earliest stages of stellar evolution, such as jet-like outflows. If tidal interactions are indeed of general importance, planet-forming discs may often have a more chaotic and violent early evolution than in standard models, and shock heating events may be common. Interactions in a hierarchy of subgroups may play a role in building up massive stars in clusters and in determining the form of the upper initial mass function (IMF) . Many of the processes discussed here have analogues on galactic scales, and there may be similarities between the formation of massive stars by interaction-driven accretion processes in clusters and the buildup of massive black holes in galactic nuclei.     

New indications of the 4-month oscillation in solar activity,atmospheric circulation and Earth's rotation

The 4-month oscillation, detected earlier by the same authors in geophysical and solar data series, is now confirmed by the analysis of other observations. In the present results the 4-month oscillation is better emphasized than in previous results, and the analysis of the new series confirms that the solar activity contribution to the global atmospheric circulation and consequently to the Earth's rotation is not negligeable. It is shown that in the effective atmospheric angular momentum and Earth's rotation, its amplitude is slightly above the amplitude of the oscillation known as the Madden-Julian cycle.     

Exchange of global mean angular momentum between an atmosphere and its underlying planet

This paper investigates the exchange of global mean angular momentum between an atmosphere and its underlying planet by a simple model. The model parameterizes four processes that are responsible for zonal mean momentum budget in the atmospheric boundary layer for a rotating planet: (i) meridional circulation that redistributes the relative angular momentum, (ii) horizontal diffusion that smoothes the prograde and retrograde winds, (iii) frictional drag that exchanges atmospheric angular momentum with the underlying planet, and (iv) internal redistribution of the zonal mean momentum by wave drag. It is shown that under a steady-state or a long-term average condition, the global relative angular momentum in the boundary layer vanishes unless there exists a preferred frictional drag for either the prograde or the retrograde zonal wind. We further show quantitatively that one cannot have either a predominant steady prograde or retrograde wind in the boundary layer of a planetary atmosphere. The parameter dependencies of the global relative angular momentum and the strength of the atmospheric circulation in the boundary layer are derived explicitly and used to explain the observational differences between the atmospheres of Earth and Venus.     

Further determinations of upper-atmosphere rotational speed from analysis of satellite orbits

The average angular velocity of the upper atmosphere, which we take as Λ times the Earth's angular velocity, can be evaluated by analysing the changes in the orbital inclinations of satellites. In this paper the nine most suitable orbits now available are analysed and values of Λ are found for heights between 200 and 260 km. The results, which are more accurate than in our previous studies, confirm that Λ 1, i.e. that the atmosphere rotates faster than the Earth at these heights, and show that Λ increases with height, from 1.1 at 210 km to 1.4 at 260 km. This corresponds to mean west-to-east winds of 30 m/s at 210 km, increasing to 130 m/s at 260 km height. Results from one satellite indicate that the wind is probably strongest at times near sunset, with Λ = 1.5 ± 0.1 at 200 km height in August 1966. Comparisons are made with previous observational results and some of the suggested theoretical explanations are outlined.     

Decadal variations in a Venus general circulation model

The Community Atmosphere Model (CAM), a 3-dimensional Earth-based climate model, has been modified to simulate the dynamics of the Venus atmosphere. The most current finite volume version of CAM is used with Earth-related processes removed, parameters appropriate for Venus introduced, and some basic physics approximations adopted. A simplified Newtonian cooling approximation has been used for the radiation scheme. We use a high resolution (1° by 1° in latitude and longitude) to take account of small-scale dynamical processes that might be important on Venus. A Rayleigh friction approach is used at the lower boundary to represent surface drag, and a similar approach is implemented in the uppermost few model levels providing a ‘sponge layer’ to prevent wave reflection from the upper boundary. The simulations generate superrotation with wind velocities comparable to those measured in the Venus atmosphere by probes and around 50-60% of those measured by cloud tracking. At cloud heights and above the atmosphere is always superrotating with mid-latitude zonal jets that wax and wane on an approximate 10 year cycle. However, below the clouds, the zonal winds vary periodically on a decadal timescale between superrotation and subrotation. Both subrotating and superrotating mid-latitude jets are found in the approximate 40-60 km altitude range. The growth and decay of the sub-cloud level jets also occur on the decadal timescale. Though subrotating zonal winds are found below the clouds, the total angular momentum of the atmosphere is always in the sense of superrotation. The global relative angular momentum of the atmosphere oscillates with an amplitude of about 5% on the approximate 10 year timescale. Symmetric instability in the near surface equatorial atmosphere might be the source of the decadal oscillation in the atmospheric state. Analyses of angular momentum transport show that all the jets are built up by poleward transport by a meridional circulation while angular momentum is redistributed to lower latitudes primarily by transient eddies. Possible changes in the structure of Venus’ cloud level mid-latitude jets measured by Mariner 10, Pioneer Venus, and Venus Express suggest that a cyclic variation similar to that found in the model might occur in the real Venus atmosphere, although no subrotating winds below the cloud level have been observed to date. Venus’ atmosphere must be observed over multi-year timescales and below the clouds if we are to understand its dynamics.     

Eddy viscosity and turbulent Schmidt number by kink-type instabilities of toroidal magnetic fields

The potential of the non-axisymmetric magnetic instability to transport angular momentum and to mix chemicals is probed considering the stability of a nearly uniform toroidal field between conducting cylinders with different rotation rates. The fluid between the cylinders is assumed as incompressible and to be of uniform density. With a linear theory, the neutral-stability maps for   m = 1  are computed. Rigid rotation must be sub-Alfvénic to allow instability, while for differential rotation also an unstable domain with faster rotation exists [azimuthal magnetorotational instability (AMRI)]. The rotational quenching of the magnetic instability is strongest for magnetic Prandtl number of the order of unity.
The effective angular momentum transport by the instability is directed outwards for subrotation. The resulting magnetic-induced eddy viscosity exceeds the microscopic values by factors of 10–100. This is only true for AMRI; in the opposite case of Tayler instability, the viscosity results are very small.
The same instability also quenches concentration gradients of chemicals by dynamic fluctuations. The corresponding diffusion coefficient always remains smaller than the magnetic-generated eddy viscosity. A Schmidt number of the order of 30 is found as the ratio of the effective viscosity and the diffusion coefficient. For not too strong magnetic fields in the radiation zone of young solar-type stars, the magnetic instability transports much more angular momentum than that it mixes chemicals.     

Resistance of motion to a small, hypervelocity sphere, sputtering through a gas

Earlier work on the resistance acting on a small sphere moving through a gas is reviewed. A model for the resistance encountered by a sphere, the surface molecules of which are sputtered off during collisions with the gas molecules, is derived and compared with the case of specular reflection. The sputtering model is applied to the case of small 10-μm radius meteoroids entering the Earth's atmosphere. A possible link between the results obtained and the recent discovery of unheated, organic grains at an altitude of 40 km in the Earth's atmosphere is considered.     

A zonal-averaged dynamical model for the middle atmosphere including gravity wave mean flow interaction: Solstice conditions

Using a set of transformed Eulerian equations the zonal-averaged circulation of the middle atmosphere (10–110 km) is calculated on a global scale for solstice conditions. The emphasis lies on an improved modelling of the zonal momentum balance of the mesophere and lower thermosphere. For this purpose an internal gravity wave mean flow interaction model suggested by T. Matsuno has been incorporated in a slightly modified version. With this model the observed reversal of the zonal wind with height in the summer upper mesosphere and lower thermosphere can be reproduced. The coefficient of eddy momentum diffusion and the Rayleigh friction coefficient used in this model have been made temperature dependent by describing them as a function of the local static stability parameter.     

Comments on the paper: Diurnal,annual and solar cycle variations of hydroxyl and sodium nightglow intensities in the Europe-Africa sector

Night-time variations of the OH nightglow intensity reported by Wiens and Weill are compared with the theoretical predictions of a number of models. The behaviour of this emission agrees better with the theoretical one for locations in the equatorial zone but becomes more variable and less predictable for mid-latitude stations. It is calculated that, as a result of an increase of the eddy diffusion coefficient K, the OH emission can deviate from the typical night-time variation and increase by a factor as high as 2 if K is multiplied by 10. It is suggested that the eddy diffusion coefficient in the upper atmosphere is lower and undergoes lower amplitude variations in the equatorial zone than in the mid-latitude regions.     

Effects of merging histories on angular momentum distribution of dark matter haloes

The effects of merging histories of proto-objects on the angular momentum distributions of the present-time dark matter haloes are analysed. An analytical approach to the analysis of the angular momentum distributions assumes that the haloes are initially homogeneous ellipsoids and that the growth of the angular momentum of the haloes halts at their maximum expansion time. However, the maximum expansion time cannot be determined uniquely, because in the hierarchical clustering scenario each progenitor, or subunit, of the halo has its own maximum expansion time. Therefore the merging history of the halo may be important in estimating its angular momentum. Using the merger tree model by Rodrigues &38; Thomas, which takes into account the spatial correlations of the density fluctuations, we have investigated the effects of the merging histories on the angular momentum distributions of dark matter haloes. It was found that the merger effects, that is, the effects of the inhomogeneity of the maximum expansion times of the progenitors which finally merge together into a halo, do not strongly affect the final angular momentum distributions, so that the homogeneous ellipsoid approximation happens to be good for the estimation of the angular momentum distribution of dark matter haloes. This is because the effect of the different directions of the angular momenta of the progenitors cancels out the effect of the inhomogeneity of the maximum expansion times of the progenitors.   The contribution of the orbital angular momentum to the total angular momentum when two or more pre-existing haloes merge together was also investigated. It is shown that this contribution is more important than that of the angular momentum of diffuse accreting matter to the total angular momentum, especially when the mergers occur many times.     

Toroidal field instability and eddy viscosity in Taylor‐Couette flows

Toroidal magnetic fields subject to the Tayler instability can transport angular momentum. We show that the Maxwell and Reynolds stress of the nonaxisymmetric field pattern depend linearly on the shear in the cylindrical gap geometry. Resulting angular momentum transport also scales linear with shear. It is directed outwards for astrophysical relevant flows and directed inwards for superrotating flows with dΩ/dR > 0. We define an eddy viscosity based on the linear relation between shear and angular momentum transport and show that its maximum for given Prandtl and Hartmann number depends linear on the magnetic Reynolds number Rm. For Rm ≃ 1000 the eddy viscosity is of the size of 30 in units of the microscopic value. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)